Comparative evaluation of displacement and stress distribution pattern during mandibular arch distalization with extra and inter-radicular mini-implants: a three-dimensional finite element study

ABSTRACT Objective: To compare the initial stress distribution and displacement on mandibular dentition using extra and inter-radicular mini-implants for arch distalization, by means of finite element analysis. Methods: For this study, two finite element models of the mandible were designed. The models consisted of periodontal ligament (PDL) and alveolar bone of all teeth until second molars. In the Case 1, bilateral extra-radicular buccal-shelf stainless steel mini-implants (10.0-mm length; 2.0-mm diameter) were placed between first and second permanent molars. In the Case 2, bilateral inter-radicular stainless steel mini-implants (10.0-mm length; 1.5-mm diameter) were placed between second premolar and first permanent molar. Power hook was attached between canine and first premolar at a fixed height of 8mm. In the two cases, 200g of distalization force was applied. ANSYS v. 12.1 software was used to analyze and compare von Mises stress and displacement in the mandibular dentition, PDL and bone. Results: Higher stresses were observed in mandibular dentition with the inter-radicular implant system. The amount of von Mises stress was higher for cortical bone (85.66MPa) and cancellous bone (3.64MPa) in Case 2, in comparison to cortical bone (41.93MPa) and cancellous bone (3.43MPa) in Case 1. The amount of arch distalization was higher for mandible in Case 1 (0.028mm), in comparison to Case 2 (0.026mm). Conclusion: Both systems were clinically safe, but extra-radicular implants showed more effective and controlled distalization pattern, in comparison to inter-radicular implants, in Class III malocclusion treatment.


INTRODUCTION
Skeletal Class III malocclusion has relatively low incidence, with a prevalence of 14% in Asians, and 1-5% in Caucasians.
The prevalence of Angle Class III malocclusion varies greatly among and within populations, ranging from 0% to 26%. 1 It was found that the most common group of Class III patients comprises normal maxilla and overdeveloped mandible. However, a smaller group of patients is also seen with underdeveloped maxilla and overdeveloped mandible. 2 As suggested by many authors, to correct anterior crossbite, mandibular anterior crowding, and mandibular dental asymmetry without extracting premolars, distalization of the mandibular teeth is the best treatment option. 3,4 The options for this approach include using reverse headgears, chin cups, functional appliances and simple fixed appliance with heavy inter-arch elastics.
The majority of the patients with severe skeletal Class III malocclusion are candidates for orthognathic surgery, which is the only choice to achieve a normal occlusion and an aesthetic profile.
However, patient may not accept the surgery, and will continue to search for fixed orthodontic treatment. 5 Class III elastics can cause unwanted side effects, such as maxillary incisor proclination, maxillary molar and mandibular incisor elongation, with tendency to expand maxillary molars, besides requiring patient compliance. To prevent these undesirable effects, absolute anchorage systems have been applied for either en-masse distalization of mandibular dentition or molar distalization. 6 When using conventional intraoral distalizing appliances, there is an adverse and unavoidable reciprocal mesial movement of the anterior teeth and premolars during distal movement of the molars. Therefore, the resultant of the distalization process for the anterior segment is a round-trip movement. 7,8 Distal movement using mini-implants allows the group movement of buccal segment teeth only: There is no forward movement of the anterior teeth in mini-implant supported biomechanics. 7,9,10 For distalization of the mandibular dentition, mini-implants can be placed in various extra-radicular and inter-radicular sites.
Elastomeric chain or NiTi close coil springs are attached to the mini-implants and the entire mandibular arch can be distalized or uprighted with minimal adverse effects. 1 Inter-radicular mini-implants for distalization of the mandibular arch can be placed in various locations, such as between the mandibular second premolar and first molar or between the mandibular first molar and second molar. 7,11 Also, extra-radicular implants like buccal shelf implants, lingual implants and retromolar pad implants, can be used for mandibular arch distalization. The finite element method (FEM) has been utilized in Dentistry and Orthodontics due to its ability to evaluate stresses of interest, using computer-aided design (CAD) models. Finite element analysis (FEA) has particularly useful applications in evaluating aspects of mini-implants used in orthodontics. 12,13 Both two-dimensional (2D) and three-dimensional (3D) stress analysis have been used to assess the dental implants. Many studies have made a comparison between the 3D and 2D FEA.
The 3D method has been shown to offer a more precise prediction of stress distribution than the 2D method. Hence, distalization treatment effect can be compared with other models using different biomechanical variables, such as displacements, strains, and stresses, by means of the finite element models. 14 No previous FEM study has evaluated the stress distribution on the mandibular teeth during distalization of the whole arch.
Thus, the aim of this study was to analyze stress distribution pattern on the mandibular teeth during distalization with extra-radicular and inter-radicular mini-implants, using a 3D finite element model of the mandible.

MATERIAL AND METHODS
Finite element analysis is a method for numerical analysis based on material properties. Finite element modeling is the representation of geometry in terms of a finite number of elements and their connection points, known as nodes, by building blocks Maheshwari A, Chawda DN, Kushwah A, Agarwal RK, Golwara AK, Dixit PB -Comparative evaluation of displacement and stress distribution pattern during mandibular arch distalization with extra and inter-radicular mini-implants: a three-dimensional finite element study for numerical representation of the model. The elements are of finite number, as opposed to a theoretical model with complete continuity. The object of interest has to be broken up into a meshwork that consists of a number of nodes on and in the object. These nodes, or points, are then connected to form a system of elements. By knowing the mechanical properties of the object, such as modulus of elasticity and Poison's ratio, one can determine how much distortion each part of the cube undergoes when other part is moved by a force. [14][15][16] The methodology used for FEM analysis is described below and presented in Figure 1 2. The required portion of mandible was considered and converted to STL format.
3. STL file was then converted to IGES data, using Rapid Form.
4. The geometric model in IGES format was further converted into finite element model using Hypermesh v.13.0 software. 5. In Hypermesh, separate modeling of bone, teeth, periodontal ligament and the implant-supported fixed appliance was done, and finally assembled together.

Material properties like elastic modulus and Poison's ratio
were assigned for teeth, periodontal ligament, bone, orthodontic brackets, implants and archwire.    Each structure was then assigned a specific material property.
The different structures in this finite element model included teeth, periodontal ligament, alveolar bone, brackets, archwire and mini-implants. The material properties used in this study were according to values given by Wheelers standard dental anatomy book (Table 1).
In this study, all the structures were assumed to be isotropic (for an isotropic material, the properties are same in all directions).

RESULTS
The result of an analysis is called post-processing. Stresses were calculated and presented in colorful areas, in which different colors represented different stress levels in the deformed state: Red color region of spectrum indicated maximum stresses/displacement, and colors such as orange, yellow, green and blue represented decreasing levels of stresses/displacement, in that order.
The results were obtained as distribution of von Mises stresses on the mandibular teeth, mandible, and periodontal ligament. Displacement of the teeth was calculated in three planes, i.e., transverse, sagittal and vertical plane, using X, Y and Z-axes, respectively. The X-axis showed bucco-lingual displacement in transverse plane, Y-axis showed distal displacement in sagittal plane, Z-axis showed displacement in vertical plane. Case 2 showed more displacement than Case 1. Figure 4 and Table 2 show more controlled movement of anterior teeth in Case 1.       E) Von mises stress contour for posterior teeth (Figs 8, 9 and Table   3): The stress recorded at the first premolar for Case 1 and Case 2 was 78.04MPa and 84.38MPa, respectively. The stress distribution at the second premolar for Case 1 and Case 2 was 11.08MPa and 12.54MPa, respectively. The stress observed at the first molar for Case 1 and Case 2 was 9.35MPa and 9.66MPa, respectively.
The stress distribution evaluated at the second molar region for Case 1 was 1.18MPa and for Case 2 was 3.36MPa.    Table 3): The stress distribution at the mandible in Case 1 for the cortical bone and cancellous bone was 41.93MPa and 3.43MPa, respectively. The stress distribution at the mandible in Case 1 for the cortical bone and cancellous bone was 85.66MPa and 3.64MPa, respectively. In the Case 2, the amount of stress in mandibular bone was higher than in the Case 1.  and Table 3

DISCUSSION
Distalization of the mandibular dentition is an effective treatment for mild to moderate adult Class III malocclusions requiring camouflage therapy. Distalization helps to achieve satisfactory results for the patient, since many patients are reluctant to consent to the surgical option -due to the increased risk and treatment financial cost. 20 Distalization is the best treatment modality for patients who aim to avoid extraction of the premolars and complicated orthognathic surgery, with long recovery time. 3,4,7,11 Combining regional acceleratory phenomenon and a mini-implant anchorage system may help in achieving satisfactory results with a shorter treatment time. Extraction of the mandibular third molars immediately before distalization may create a regional acceleratory phenomenon, and help to speed up tooth movements. Puncturing cortical bone in localized areas during mini-implant-assisted retraction may potentially create a regional acceleratory phenomenon. It is observed that mini-implant failure may occur when a regional acceleratory phenomenon is created near the implant site. 1 Mini-implants can be used in mandibular arch to distalize the mandibular dentition and achieve proper occlusion in Class III patients. 3,7,11 The mini-implant placement in retromolar pad area is dependent on the local anatomy of the mandible and the soft tissue thickness in that area. It is often difficult to place retromo- Also, it is recommended to place the implant as low as possible near the center of resistance on the mandibular dentition to gain ideal vertical control, which is not possible in case of retromolar pad mini-implant. 22 Whereas, while placing the buccal shelf implant, increasing the vertical level or insertion angle results in a higher cortical bone thickness and distance from molar root, which is considered a safe and reliable implant placement site. 18 The current study compared buccal shelf mini-implant distalization and inter-radicular mini-implant distalization, and it was carried out simulating the clinical condition by applying distalizing force to the mandibular dentition. The stress distribution The displacement in Y-axis indicates the movement of the teeth in the mesio-distal direction. Both mini-implant types provided force system that drove the mandibular dentition in distal direction. However, the evaluated displacement (Fig 7, Table 2) of the teeth was higher in the Case 1. In the literature, the max-

CONCLUSION
In the 3D finite element analysis of stress distribution pattern during distalization of the mandibular dentition using two different types of mini-implant biomechanics in adult patient, the following conclusions can be made: » The Case 2 (inter-radicular mini-implants) produced higher stress at the tooth, bone and PDL; when compared to the Case 1 (extra-radicular mini-implants), but results were within ultimate tensile limit, being considered clinically safe.
» For anterior teeth, Case 2 showed more movement along Y-axis, except for central incisor, which was the same for both cases. » Comparing the adverse side-effects in X-axis, a tendency of the posterior segment to move buccally was observed to be more intense in Case 2, except for the second premolar.
» Comparing the adverse side-effects in Z-axis, the tendency of posterior segment intrusion and anterior segment extrusion was observed to be more intense in Case 2.
» In Case 1, there was a significant amount of distance maintained between the roots of the teeth and the mini-implants, avoiding any need to relocate them.
In the vertical dimension, in comparison to the insertion point of the inter-radicular mini-implant (Case 2), the insertion point of the buccal shelf implant (Case 1) was closer to the center of resistance (C R ) of mandibular dentition; therefore, the line of distalizing force would be closer to the C R in Case 1 and would be nearly parallel to the occlusal plane. Therefore, distalizing the mandibular dentition using a buccal shelf implant will result